1. Field of the Invention
The present invention pertains generally to controlling the operation of aeroengine compressors, and more particularly to a method and apparatus for predicting on the onset of stall and then using an extremum seeking controller to stabilize stall.
2. Description of the Background Art
The mainstream methods of adaptive control for linear [1,9,12] and nonlinear [17] systems are applicable only for regulation to known set points or reference trajectories. In some applications, the reference-to-output map has an extremum (w.l.o.g. we assume that it is a maximum) and the objective is to select the set point to keep the output at the extremum value. The uncertainty in the reference-to-output map makes it necessary to use some sort of adaptation to find the set point which maximizes the output. This problem, called "extremum control" or "self-optimizing control," was popular in the 1950's and 1960's [4,6,8,13,14,26,27,29], much before the theoretical breakthroughs in adaptive linear control of the 1980's. In fact, the emergence of extremum control dates as far back as the 1922 paper of Leblanc [19], whose scheme may very well have been the first "adaptive" controller reported in the literature. Among the surveys on extremum control, we find the one by Sternby [31] particularly useful, as well as Section 13.3 in Astrom and Wittenmark [1] which puts extremum control among the most promising future areas for adaptive control. Among the many applications of extremum control overviewed in [31] and [1] are combustion processes (for IC engines, steam generating plants, and gas furnaces), grinding processes, solar cell and radio telescope antenna adjustment to maximize the received signal, and blade adjustment in water turbines and wind mills to maximize the generated power. A more recent application of extremum control are anti-lock braking systems [5]. On the theoretical forefront, the studies of Meerkov [22,23,24] stand out.
The idea to use extremum control for maximizing the pressure rise in an aeroengine compressor is not new. As far back as in 1957, George Vasu of the NACA (now NASA) Lewis Laboratory published his experiments in which he varied the fuel flow to achieve maximum pressure [33]. While his engine was apparently not of the kind that could enter either rotating stall or surge instabilities (so local stabilizing feedback was not necessary), he recognized the opportunity to maximize the pressure by extremum seeking feedback long before the compressor models of the 1970's and 1980's emerged and the dynamics of compression systems were understood.
However, most of the results available on extremum control consider a plant as a static map. A few references approach problems where the plant is a cascade of a nonlinear static map and a linear dynamic system (the so-called Hammerstein and Wiener models), see [35] and references therein.
In a jet engine, the role of a compressor is to provide pressure rise to the combustor. The pressure rise is a function of throttle opening. This function is not monotonic, it has a maximum, i.e., there is a physical limit to the level of pressure that can be achieved at the compressor exit. The objective is to operate the compressor at its maximum pressure so that a smaller compressor can be employed to achieve a desired thrust.
There are two problems associated with the objective of achieving maximum pressure.
First, even if we know the location of the maximum, i.e., the throttle opening which gives the maximal pressure rise, this pressure cannot be achieved with a constant throttle opening because of compressor instabilities, rotating stall and surge, that occur for values of the throttle opening near the maximizing value. In this regard, it is known that active control can be used to stabilize rotating stall and surge. Active control consists of measuring the pressure in the compressor (in various places) and varying the throttle opening as a function of these instabilities in an intelligent way which stabilizes the rotating stall and surge instabilities.
Second, even when rotating stall and surge instabilities are removed using throttle opening that varies as a function of pressure measurements, the mean pressure rise may be below the physically achievable maximum value because of various perturbations and changes/uncertainties in the operating regime. Thus, the main problem that remains is (in very simplified terms) how to determine the mean value of the throttle opening--"the DC component"--to maximize the pressure rise (in addition to the "AC component" which we referred to as the rotating stall and surge control in the previous paragraph).
If a compressor were a static and stable system whose input/output representation is a function that has a maximum, one would employ standard "extremum seeking" (also known as "optimum seeking, extremum searching, hill climbing, optimalizing, etc.") feedback schemes which would guarantee that the system would operate near the maximum of the output variable. The difference between the compressor and these standard problems is that compressor is not a static but a dynamic system, and that it is not (open-loop) stable but unstable in the high-pressure regime.